


from itertools import product
def 							UpperCamelCase_(					_A :int					,  _A :int	)->		list[int]:
			UpperCamelCase__       =							sides_number
			UpperCamelCase__       =							max_face_number * dice_number
			UpperCamelCase__       =							[0] * (max_total + 1)

			UpperCamelCase__       =							1
			UpperCamelCase__       =							range(_A					,  max_face_number + 1	)
			for dice_numbers in product(_A					,  repeat=_A	):
						UpperCamelCase__       =							sum(_A	)
						totals_frequencies[total] += 1

			return totals_frequencies
def 							UpperCamelCase_(					)->		float:
			UpperCamelCase__       =							total_frequency_distribution(
			    sides_number=4					,  dice_number=9	)
			UpperCamelCase__       =							total_frequency_distribution(
			    sides_number=6					,  dice_number=6	)

			UpperCamelCase__       =							0
			UpperCamelCase__       =							9
			UpperCamelCase__       =							4 * 9
			UpperCamelCase__       =							6
			for peter_total in range(_A					,  max_peter_total + 1	):
						peter_wins_count += peter_totals_frequencies[peter_total] * sum(
						    colin_totals_frequencies[min_colin_total:peter_total]	)

			UpperCamelCase__       =							(4**9) * (6**6)
			UpperCamelCase__       =							peter_wins_count / total_games_number

			UpperCamelCase__       =							round(_A					,  ndigits=7	)

			return rounded_peter_win_probability


if __name__ == "__main__":
						print(f'''{solution() = }''')






import gc
import unittest

from diffusers import FlaxControlNetModel, FlaxStableDiffusionControlNetPipeline
from diffusers.utils import is_flax_available, load_image, slow
from diffusers.utils.testing_utils import require_flax


if is_flax_available():
						import jax
						import jax.numpy as jnp
						from flax.jax_utils import replicate
						from flax.training.common_utils import shard







@slow
@require_flax
class 							lowerCamelCase__						(				unittest.TestCase   ):






			"""simple docstring"""






			def 					snake_case__					(				self  ):

						'''simple docstring'''


						super().tearDown()
						gc.collect()




			def 					snake_case__					(				self  ):

						'''simple docstring'''


						UpperCamelCase__,   UpperCamelCase__       =							FlaxControlNetModel.from_pretrained(
						    "lllyasviel/sd-controlnet-canny"   ,    from_pt=snake_case   ,    dtype=jnp.bfloataa  )
						UpperCamelCase__,   UpperCamelCase__       =							FlaxStableDiffusionControlNetPipeline.from_pretrained(
						    "runwayml/stable-diffusion-v1-5"   ,    controlnet=snake_case   ,    from_pt=snake_case   ,    dtype=jnp.bfloataa  )
						UpperCamelCase__       =							controlnet_params

						UpperCamelCase__       =							"bird"
						UpperCamelCase__       =							jax.device_count()
						UpperCamelCase__       =							pipe.prepare_text_inputs([prompts] * num_samples  )

						UpperCamelCase__       =							load_image(
						    "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/sd_controlnet/bird_canny.png"  )
						UpperCamelCase__       =							pipe.prepare_image_inputs([canny_image] * num_samples  )

						UpperCamelCase__       =							jax.random.PRNGKey(0  )
						UpperCamelCase__       =							jax.random.split(snake_case   ,    jax.device_count()  )

						UpperCamelCase__       =							replicate(snake_case  )
						UpperCamelCase__       =							shard(snake_case  )
						UpperCamelCase__       =							shard(snake_case  )

						UpperCamelCase__       =							pipe(
						    prompt_ids=snake_case   ,    image=snake_case   ,    params=snake_case   ,    prng_seed=snake_case   ,    num_inference_steps=50   ,    jit=snake_case   ,    ).images
						assert images.shape == (jax.device_count(), 1, 768, 512, 3)

						UpperCamelCase__       =							images.reshape((images.shape[0] * images.shape[1],) + images.shape[-3:]  )
						UpperCamelCase__       =							images[0, 253:256, 253:256, -1]

						UpperCamelCase__       =							jnp.asarray(jax.device_get(image_slice.flatten()  )  )
						UpperCamelCase__       =							jnp.array(
						    [0.167969, 0.116699, 0.081543, 0.154297, 0.132812, 0.108887, 0.169922, 0.169922, 0.205078]  )
						print(F'''output_slice: {output_slice}'''  )
						assert jnp.abs(output_slice - expected_slice  ).max() < 1E-2







			def 					snake_case__					(				self  ):

						'''simple docstring'''


						UpperCamelCase__,   UpperCamelCase__       =							FlaxControlNetModel.from_pretrained(
						    "lllyasviel/sd-controlnet-openpose"   ,    from_pt=snake_case   ,    dtype=jnp.bfloataa  )
						UpperCamelCase__,   UpperCamelCase__       =							FlaxStableDiffusionControlNetPipeline.from_pretrained(
						    "runwayml/stable-diffusion-v1-5"   ,    controlnet=snake_case   ,    from_pt=snake_case   ,    dtype=jnp.bfloataa  )
						UpperCamelCase__       =							controlnet_params

						UpperCamelCase__       =							"Chef in the kitchen"
						UpperCamelCase__       =							jax.device_count()
						UpperCamelCase__       =							pipe.prepare_text_inputs([prompts] * num_samples  )

						UpperCamelCase__       =							load_image(
						    "https://huggingface.co/datasets/hf-internal-testing/diffusers-images/resolve/main/sd_controlnet/pose.png"  )
						UpperCamelCase__       =							pipe.prepare_image_inputs([pose_image] * num_samples  )

						UpperCamelCase__       =							jax.random.PRNGKey(0  )
						UpperCamelCase__       =							jax.random.split(snake_case   ,    jax.device_count()  )

						UpperCamelCase__       =							replicate(snake_case  )
						UpperCamelCase__       =							shard(snake_case  )
						UpperCamelCase__       =							shard(snake_case  )

						UpperCamelCase__       =							pipe(
						    prompt_ids=snake_case   ,    image=snake_case   ,    params=snake_case   ,    prng_seed=snake_case   ,    num_inference_steps=50   ,    jit=snake_case   ,    ).images
						assert images.shape == (jax.device_count(), 1, 768, 512, 3)

						UpperCamelCase__       =							images.reshape((images.shape[0] * images.shape[1],) + images.shape[-3:]  )
						UpperCamelCase__       =							images[0, 253:256, 253:256, -1]

						UpperCamelCase__       =							jnp.asarray(jax.device_get(image_slice.flatten()  )  )
						UpperCamelCase__       =							jnp.array(
						    [[0.271484, 0.261719, 0.275391, 0.277344, 0.279297, 0.291016, 0.294922, 0.302734, 0.302734]]  )
						print(F'''output_slice: {output_slice}'''  )
						assert jnp.abs(output_slice - expected_slice  ).max() < 1E-2


